A186716 Irregular triangle C(n,k): the number of connected k-regular graphs on n vertices having girth at least six.

1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 5, 0, 0, 1, 0, 0, 0, 1, 32, 0, 0, 1, 0, 0, 0, 1, 385, 0, 0, 1, 0, 0, 0, 1, 7574, 0, 0, 1, 0, 0, 0, 1, 181227, 1, 0, 0, 1, 0, 0, 0, 0, 1

Offset: 1

Author

Jason Kimberley, Nov 23 2011

Keywords

• nonn
• hard
• tabf

Comments

Other than the first two rows, each row begins with 0, 0, 1.

Examples

			1;
0, 1;
0, 0;
0, 0;
0, 0;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1, 1;
0, 0, 1, 0;
0, 0, 1, 1;
0, 0, 1, 0;
0, 0, 1, 5;
0, 0, 1, 0;
0, 0, 1, 32;
0, 0, 1, 0;
0, 0, 1, 385;
0, 0, 1, 0;
0, 0, 1, 7574;
0, 0, 1, 0;
0, 0, 1, 181227, 1;
0, 0, 1, 0, 0;
0, 0, 1, 4624501, 1;
0, 0, 1, 0, 0;
0, 0, 1, 122090544, 4;
0, 0, 1, 0, 0;
0, 0, 1, 3328929954, 19;
0, 0, 1, 0, 0;
0, 0, 1, 93990692595, 1272;
0, 0, 1, 0, 25;
0, 0, 1, 2754222605376, 494031;
0, 0, 1, 0, 13504;
		

References

• M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146.

Links

• Jason Kimberley, Rows n = 1..37 of triangle, flattened
• House of Graphs, Cubic graphs
• Jason Kimberley, Connected regular graphs with girth at least 6
• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
• M. Meringer, Tables of Regular Graphs
• M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146.

Crossrefs

Connected k-regular simple graphs with girth at least 6: A186726 (any k), this sequence (triangle); specific k: A185116 (k=2), A014374 (k=3), A058348 (k=4).

Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth at least g: A068934 (g=3), A186714 (g=4), A186715 (g=5), this sequence (g=6), A186717 (g=7), A186718 (g=8), A186719 (g=9).

Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth exactly g: A186733 (g=3), A186734 (g=4).

Extensions

C(36,3) from House of Graphs via Jason Kimberley, May 21 2017